Question

here is a rectangular pyramid. round answers in the problem to the nearest tenth if necessary. a. what is the height of the pyramid? units. b. what is the volume of the pyramid? units.

Explanation:

Step1: Find the height using Pythagorean theorem

Let the height be $h$. The base - related right - triangle has a hypotenuse of 13 cm and one leg of 4 cm. According to the Pythagorean theorem $a^{2}+b^{2}=c^{2}$, where $c = 13$ and $a = 4$. So $h=\sqrt{13^{2}-4^{2}}=\sqrt{169 - 16}=\sqrt{153}\approx12.4$ cm.

Step2: Calculate the base area of the rectangular pyramid

The base of the rectangular pyramid has length $l = 10$ cm and width $w = 4$ cm. The base area $B=l\times w=10\times4 = 40$ $cm^{2}$.

Step3: Calculate the volume of the rectangular pyramid

The volume formula of a pyramid is $V=\frac{1}{3}Bh$, where $B$ is the base area and $h$ is the height. Substitute $B = 40$ $cm^{2}$ and $h\approx12.4$ cm into the formula. So $V=\frac{1}{3}\times40\times12.4=\frac{496}{3}\approx165.3$ $cm^{3}$.

Answer:

A. 12.4
B. 165.3